Subgraph-finding problems involve identifying patterns in structured data. In theory these problems should be computationally hard for an algorithm to solve, but in practice intelligent constraint-based algorithms can quickly solve even large problems. This research will uses scientific (rather than purely mathematical) techniques to increase our understanding of this gap between theory and practice, and will allow us to design better algorithms in the future. The research is based upon analysing proof logs, which are a mathematical description of how an algorithm reached its answer.